This is a classic calculus problem that has been "backmapped" to algebra 1. Students build a box with a top using 12 x 18 construction paper and a given size for the corner cut. They calculate the volume of the box. Each group has a different sized corner cut - creating different sized boxes.
Elementary Connections
During the workshop, someone asked about how to connect polynomials to elementary.
In the 4th grade Investigations, students begin visualizing arrays (Grade 4, Unit 3, Multiple Towers and Division Stories) and then begin representing multiplication with arrays (Grade 4, Unit 8, How Many Packages? How Many Groups?)
Information about general form to vertex form:
Elementary Connections
During the workshop, someone asked about how to connect polynomials to elementary.
In the 4th grade Investigations, students begin visualizing arrays (Grade 4, Unit 3, Multiple Towers and Division Stories) and then begin representing multiplication with arrays (Grade 4, Unit 8, How Many Packages? How Many Groups?)
http://investigations.terc.edu/library/curric-gl/teaching_g4_2ed.pdf